Statistical Blackjack Analyzer

Statistical Blackjack AnalyzerWindows Software by Karel Janecek

Version 5.x Information
Basic Information About SBA 5.0

ARCHIVEDStatistical Blackjack Analyzer (SBA) is (was) a very powerful blackjack simulator which provides you with a lot of interesting and very useful information about the game. Data from SBA’s simulations are used in John Auston’s software Blackjack Risk Manager 2000.

SBA is by far the fastest existing commercial blackjack simulator. SBA runs 10 million rounds per MINUTE on PII/266Mhz, which is more than 1 billion rounds in two hours. This is in order of 10 times faster than any other available software. The speed is even higher for unbalanced counts without the true count conversion. You can run up to 100 billion rounds per simulation.

A feature of SBA is the precise strategy generator. You just enter your counting system, rules, and SBA will find all desired playing indices for you. Once the playing indices are generated, you can immediately run simulations using them! No adjustments necessary. SBA can generate composition dependent indices, including special indices like for example surrender 8,8 vs. 10 up (where the alternative is splitting rather than stand/hit). SBA can also generate indices to any fraction of the true count (up to tenths)! The indices generator plays at the speed of 90 million pairs of hands per minute on Pentium II/266.

The new feature of SBA 5.0 is the automatic Kelly risk-averse indices generator. This is a revolutionary new feature, which is not available in any other blackjack simulator. The risk averse indices significantly improve your play. This can be seen by a simulation and comparing a correct measure of performance, like for example Desirability Index or SCORE.

Part of the full version of SBA is the Explanation of Blackjack Statistics document. This electronic book explains in detail the important notions in blackjack: advantage, standard deviation, how to calculate the optimal bets, risk-of-ruin, the importance of risk-averse strategy indices, and more.

Detailed information about SBA 5.0

The output of SBA simulation is a text report file. You can see sample of SBA’s report file: SBA’s Report File

And here is the Explanation to the report file

SBA will allow you to analyze the game of blackjack for a wide range of casino conditions and practically all existing rules. You can use an arbitrary counting system with (or without) matrices for playing departures from basic strategy. SBA will tell you exactly what your advantage (or disadvantage) and risk are.

The latest version of SBA supports the ace-side count for both playing and betting adjustments. Furthermore, the new version supports secondary count, again for both playing and betting adjustments. In fact, you can combine the main count, secondary count, and ace-side count.

If you do not have playing matrices, SBA’s strategy generator will create them for you. Note, that the indices generated by SBA are precise (within random, sample error, of course.) If SBA gives different indices than your book or any other software than the indices generated by SBA are the correct indices. The Kelly risk-averse indices, which SBA can generate, are the optimal indices that one should use. An exception could be a high roller who is not allowed to bet as much as he would like to, from practical reasons. Such a person could use the expectation maximizing indices rather than risk-averse indices. Optimally, such a person should still use risk-averse indices but set ‘Aversion ratio’ in SBA to some value greater than one.

Note: To generate precise indices, you need to set precision to 3 sigma or more

With SBA, you can run practically an unlimited number of hands in one simulation. The technical constraint is set in SBA menus to 100 billion rounds. You can run any number of simulations simultaneously, which further increases the total effective speed.

SBA can simulate play under almost all varieties of casino conditions and rules. You can set different betting strategies, where the bets can be arbitrary fractions of your unit bet. You can also analyze cover betting, where the bets depend on the result of previous hands.

You can set an arbitrary state of the deck too. This way you can analyze games like Spanish 21, where the tens are removed (only J,Q,K are in the deck). SBA supports also rules common in Spanish 21 (lost ties, redouble option, etc.) You can analyze what effect on your advantage would removement of aces (or any other cards) have, or what effect would addition of any cards into the deck have.

The “Wonging” and “Anti-Wonging” features (leaving the shoe/deck on negative counts) are worked out in detail. You can leave the deck depending not only on the true count, but also on how many cards have already been dealt (how deep in the shoe you are.) This is extremely useful for unbalanced counts. You can also simulate backcounting by betting zero units on some true counts. All statistics is adjusted for this case.

You can set penetration as the number of rounds or number of cards played, or both.

You can play a different number of hands depending on the count. Furthermore, you can set the actions of other players, who play one of three available strategies (no-bust, mimic-the-dealer, or Basic). You can seat the players and yourself (the counter) at any position you want. This way you can see what effect more players have on your advantage.

You can also set your bankroll, and see what the probability of doubling it (or tripling, or whatever you want) is. This way you can analyze risk-of-ruin by a simulation.

SBA has some other features, which make the simulations very close to a real casino game. For example, you can estimate the number of decks remaining (for true count conversion). You can estimate the remaining decks to one deck, halves of a deck, thirds, quarters, etc. Of course, you can calculate the true count exactly too.

You can also set whether you round, truncate, or floor when calculating the true count for playing and betting decisions. This is an important feature since some blackjack authors use truncating, other prefer rounding, and the modern and most effective approach is flooring. SBA strategy generator can derive playing indices for all these cases.

You can analyze both face up and face down games by simply toggling a switch.

SBA is not only superior in speed but also in the amount of information and data it provides. You can observe all statistics with respect to each true count (TC) (or running count)! Not only that, you can also obtain the statistics with respect to any fraction of a TC, while the simulation does not slow down at all!

What is further absolutely unique about SBA compared to other simulators:

You get not only the advantage at each TC (or fraction of a TC), but also the standard deviation (risk estimate) for a hand played at the true count. This information allows you to calculate exactly the optimal bet at each TC. I describe in detail how to do this in a document accompanying the full version of SBA called Explanation of Blackjack Statistics.

Using this information, you can further make a fair comparison of the betting power of alternative counting systems. The betting power cannot be compared fairly, unless you know the standard deviation for each TC. Similarly, you cannot exactly calculate optimal bets unless you have this info, which presently only SBA and no other commercial simulator can provide.

The reason why SBA can do all that while keeping a superior speed is of a technical nature. SBA calculates the standard deviations most efficiently using all information from a simulation. SBA does not simulate the standard deviation using a general statistical formula, as other simulators do. Calculating is not only much faster (it actually doesn’t take any time, since you calculate at the end of the simulation), but it is also the optimal approach and more exact approach. However, this approach is mathematically complicated and is much more difficult to program than the usual one.

SBA follows a multitude of statistics, all with respect to each true (running) count or to each true count adjusted for an ace side countw. For example: correlation (measure of dependence) between two hands, which allows you to calculate optimal bets for multiple hands, statistics for pushes, doubles, advantage on insurance, etc., etc. This additional information is provided in conjunction with the standard error.

SBA is not only powerful, but also user friendly as much as a program can be with a detailed help and nicely built menu structure.

By purchasing SBA, you will not only get a powerful blackjack simulator, but you can also educate yourself in blackjack and blackjack statistics, if you want to. Among the help topics you can find a document called Explanation of Blackjack Statistics, which explains important blackjack statistics. You get to know how to optimally wager your bet, whether to play multiple hands and how to bet on multiple hands, and more.

The Explanation of Blackjack Statistics document is a part of the full version of SBA. Some parts of the document are generally known facts, some of it is based on my e-mail discussions with several blackjack experts, and some are my own insights. Some parts of the document were also posted by me on newsgroup Rec.gambling.blackjack.

Below is the content of the Explanation of Blackjack Statistics document:

I. What is Advantage and How to Calculate It

II. Standard Deviation and What It Tells Us
    1. What is a standard deviation?
    2. Practical quantitative examples for a blackjack player
    3. The second meaning of the standard deviation

III. Calculating a Confidence Interval for Expected Winnings

IV. How to Calculate an Optimal Bet

V. Correlation Coefficient and Optimal Multiple Hands Betting
    1. Should one play multiple hands?
    2. Correlation coefficient
    3. Calculating optimal bets for multiple hands

VI. Risk of Ruin Calculation

VII. How to Fairly Compare the Power of Two Counting Systems

All the text is, I believe, a source of very important information for a serious blackjack player. Note that SBA can also serve you as a reference, like a book. The truth is that you would hardly find some of the information provided in the SBA’s document in any blackjack book.

SBA is a serious analytical tool. It is not a practice tool, so you cannot play blackjack with it. For practicing blackjack, there are other nice programs on the market.

Risk-Averse Indices

Risk-averse indices were first proposed by Joel Friedman in early 80s. The importance of the risk-averse indices was underestimated and the indices were not much used in practice until recently, when the feature of risk-averse indices generation was included in SBA. The basic idea behind risk-averse indices is that when making a playing decision the player should not always maximize the expected (average) profit, but should also take the possibly increased risk into consideration.

Simulations run by several blackjack experts, John Auston among others, show that the correct usage of risk-averse indices improves player’s performance by about 3%. Now, you may think that 3% is not that much, and may not be worth the extra trouble. In general this could be true. But the point is that the 3% improvement comes with practically no extra effort! The only change is that few indices have different numbers. Today players strive to achieve extra few percent improvement and are often willing to change their counting system. Here you can reach the same improvement by just changing, say, 10 index numbers.

Kelly risk-averse indices is an absolutely unique feature that no other publicly available software other than SBA can accomplish. For example, do you know the
Hi-Lo multiple decks index for doubling hard 10 vs. dealer’s ten up? If you say +4 then you are only partially correct. This is the expectation-maximizing index.
However, it is not the optimal index. If you take the risk into consideration it turns out that the correct index is +8, which is quite a difference! This is true unless you are from some reason under-betting. Or, did you know that it is NOT correct to split 4,4 vs. 6 up for true counts greater than +6, DAS allowed? The correct
alternative is hard doubling. The reason why this is so comes from the fact that hard doubling is less risky than splitting with DAS, and this lower risk is more
significant than the small loss in expectation.

The Kelly risk-averse indices, which SBA can generate, are the optimal indices that one should use. An exception could be a high roller who from practical reasons cannot bet as much as he would like to. Such a person could use the expectation maximizing indices rather than risk-averse indices. Optimally, such a person should still use risk-averse indices but set ‘Aversion ratio’ in SBA to some value greater than one.


I believe that SBA is a bargain given its features. Especially if you compare its power/price ratio to other blackjack simulators on the market.

You can purchase one of two editions of SBA:


The standard edition runs all simulations and supports all features as mentioned above except it does not include the strategy generator. The standard edition may be sufficient for a blackjack player who needs to evaluate different rules and casino conditions, and get information about his/her expected win and associated risk, but does not necessarily need precise strategy indices and the indices published in the books are sufficient for him/her.


The advanced edition does everything what the standard edition, plus it includes a precise strategy generator that can also generate the Kelly risk-averse indices. This version can generate playing indices (even composition dependent) for any counting system and practically all existing rules.

Technical Details

SBA 5.0 requires Windows 95, 98, NT, or Windows 2000, about 5MB of hard disk space, and a PC compatible computer 486 or higher. Pentium 150Mhz or more is recommended.

Download a FREE demo version

You can download a demo version of SBA 5.0 for free.  Click here to download a demo of SBA.

The demo version looks like the full version but it allows you to run simulations with only a fixed set of rules. The strategy generator cannot be run with the demo version.

The rules supported by the unregistered version are 6 decks, penetration 250 cards, DOA, DAS, European no hole card, and early surrender. I know that these
rules are not much practical. Please purchase the full version! The demo version does not further contain the document Explanation of Blackjack Statistics, which
explains how to understand all the statistics (advantage, standard deviation, etc.), how to calculate optimal bets from simulation data, how to optimally bet on multiple hands, and other important information. The document Explanation of Blackjack Statistics is an important part of the full version.

Nevertheless, by playing with the demo version you will see how SBA exactly works and how much it can do.

To setup Statistical Blackjack Analyzer 5.0 for Windows follow these steps:

Download the SBADemo55.exe file. (With some browsers you need to click the link while holding Shift button.)
Install it – run the SBADemo55.exe file (double click) and follow the instructions.
Enjoy it – note that this is a demonstration version only and it is provided for evaluation purposes only. It has some restrictions but it can give you an idea how full version of SBA works.


Last Update: 04/05/05


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